Mortality InequalitySam PeltzmanBooth School of BusinessUniversity of Chicago

1

OverviewOverview

• Economists interested in ‘inequality’• Usually= ‘income inequality’

• Focus here: years of life• Several Questions

• How can we measure this kind of inequality?• In a metric comparable to income inequality measures?

• What has happened over time?• And how does this compare to income inequality trends?

• How does inequality of lifetimes vary• Across countries?• Across genders?

• What can we say about future trends? 2

Mortality Inequality & Income Inequality

• Income inequality is one dimension of overall inequality

• Potentially misleading as measure of personal welfare• Income measured at a moment (year)• Number of years over which income enjoyed is also important

• Think of lifetime income (consumption) (Y)

3

Y C X C = annual income or Consumption

X = number of years lived

Inequality of Mortality as a Component of Inequality of Lifetime Income

• Variability of Y across individuals in a population

• c, x are logs, so y = c+x• V=variance, S=standard deviation, r= correlation

• S(c) is a standard measure of income inequality

• This talk focuses on S(x) (or V(x))

• Entirely descriptive• How important is inequality of lifetimes compared to inequality of income?• Historically? Today?• Gender & Cross-Country Aspects

4

( ) ( ) ( ) 2 ( , ) ( ) ( )V y V c V x r c x S c S x

How Has Broad Topic Been Treated in Past?

• Most attention to cross-country comparisons • Correlation of average c and average x

• Correlation is positive, but becomes weak beyond low level (Preston)

• Change over time in average c and average x• Both increasing everywhere• But, % increase in x for low income countries > for high income• Reverse may be true for income• So: Widening “North-South” divide is exaggerated (Becker et al)

• This talk is entirely about within country comparisons• S(x) measures “does someone born today live to age 1? 25? 85?”• How has this changed over time?• Gender differences

5

Some Broad Conclusions

• Historically (since c.1750) S(x) has been important component of total inequality• More important than S(c), by some measures• S(x) has declined over time as E(x) has increased

• But relation between longevity and inequality is not necessarily monotonic • “Kuznets curve” for mortality

• Today: S(x) << S(c) in developed world• But remains important in less developed countries

• Gender inequality: long cycles, but no long trend

• The Soviet/Russian anomaly6

Measuring Mortality Inequality

• Start with Life Table• Survivors = F(age), F(0)=100,000 and F(110)=0• ‘Period’ v ‘Cohort’

• Period LT just summarizes contemporary mortality• No ‘productivity’ adjustment

• Example

7

Life Table for England, 1850

0

10000

20000

30000

40000

50000

60000

70000

80000

90000

100000

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110

Age

Su

rviv

ors

8

Measuring Mortality Inequality

• Start with Life Table• Survivors = F(age), F(0)=100,000 and F(110)=0• ‘Period’ v ‘Cohort’

• Period LT just summarizes contemporary mortality• No ‘productivity’ adjustment

• Example

• Take first difference: mortality = - ΔF = deaths between age t and t+1• Expected value of the distribution of mortality is “life expectancy at birth”

(c. 70+ years today)

• Measure dispersion around expected value

9

Measurement Issues

• Distribution of mortality is skewed left• S(log age) dominated by infant mortality• But directly comparable to S(log income)

• Show S(log age), but also take out infant mortality• E.g., age 5+

10

Prologue: How Large is Income Inequality Historically?

• If y = c+x• What is V(c) (or S(c)) within a country?

• In principle, c should be present value of future consumption at birth• In practice, all we have is per capita or per household income

• V of income probably overstates V(c)

• And, poor data on income distributions until recently

• Rough estimates• Today: .6 < S(log income) < 1• Since c.1900 upper bound ~ 1• Compare Sweden & US (i.e., high and low equality)

11

Standard Deviation of Log Household Income: US and Sweden

12

Prologue 2: What has Happened to Average Longevity?

• Increasing

• But Where? And When did this Start?

• Everywhere in the Developed World since c.1850• Steady Convergence

• Will show data for 10 countries with life tables from 1850 or before• Scandinavia + Large European + US

13

Expected Years of Life at Birth: 10 Countries

14

What has Happened to S(x) since 1750?

• Overall Measure (incl Infant mortality)• ~1.5 up to c. 1900• Declines substantially throughout 20th Century• Now ~ .3 (i.e., << income inequality measures)

15

Standard Deviation Log Life at Birth: 10 Countries

16

What has Happened to S(x) since 1750?

• Overall Measure (incl Infant mortality)• ~1.5 up to c. 1900• Declines substantially throughout 20th Century• Now ~ .3 (i.e., << income inequality measures)

• Excluding Infant Mortality (S(log life/x ≥ 5)• Similar pattern (accelerated decline after 1900)• Goes from .6 - .7 before 1900 to ~ .25 today

17

SD Log Life for Survivors to Age 5: 10 Countries

18

What has Happened to S(x) since 1750?

• Overall Measure (incl Infant mortality)• ~1.5 up to c. 1900• Declines substantially throughout 20th Century• Now ~ .3 (i.e., << income inequality measures)

• Excluding Infant Mortality (S(log life/x ≥ 5)• Similar pattern (accelerated decline after 1900)• Goes from .6 - .7 before 1900 to ~ .25 today

• Both measures converge across countries

• S(x) historically important component of inequality• Much less so today

19

Why did Inequality Improvement Lag?

1. Medical Progress (as we have so far known it) is uneven• Most of the progress is getting people to live into their 80s• Relatively little progress in extending upper limit• Example: England 1842-2002

20

Mortality Data for England/Wales 1842-2002

21

YearPercentage Surviving

Past 80Average Age at Death of Those

DyingRatio of Old to

Young

  of Births if Alive at 5 Before 80 After 80 Life Expectancy

      All Alive at 5      

  (1) (2) (3) (4) (5) (5)/(3) (5)/(4)

1842 9.6% 13.0% 36.5 50.7 85.0 2.33 1.68

1902 11.9 15.1 43.2 56.3 84.6 1.96 1.50

1952 30.1 31.1 62.2 65.1 85.3 1.37 1.31

2002 54.8 55.2 66.3 67.2 87.7 1.31 1.31

Why did Inequality Improvement Lag?

1. Medical Progress (as we have so far known it) is uneven• Most of the progress is getting people to live into their 80s• Relatively little progress in extending upper limit• Example: England 1842-2002

2. This uneven progress conflicting effects on inequality• Reducing mortality at ‘young’ ages reduced inequality• BUT increased odds of surviving to old age greater inequality

22

Medical Progress & Inequality (continued)

• Decompose X as

• X= expected life,• A1 (A2) =years lived if you die before (after) 80

• P = probability of living to 80

• Then the trend in V(log X) is

• D= log (A2/A1)

• Second term is a “Kuznets curve” in mortality• If progress means “more people survive to old age”• Then progress more inequality as long as p<1/2

• Actual progress is a mix of strictly declining first term and Kuznets effect• Kuznets effect still important in less developed world

23

1 2(1 )X p A pA

2( )2 (1 ) (1 2 )

dV x dD dpp p D p

dt dt dt

Summary So Far

• Improvement in Mortality Inequality is an Important Part of any Increase in Social Equality• Ex-infant mortality: S(x) improves ~ .3 to .4 since 1850 or 1900• Matches plausible decline in S(c) in advanced welfare states• Accounts for ~all improvement in US

• Convergence in longevity & equality across developed countries• May suggest reduction in income-longevity correlation• But incomes have also converged

24

What About Less-Developed Countries

• Mostly 20th century data• And few very poor countries

• Progress in E(x) and S(x)

• But << convergence than rich countries

• And ‘Kuznets effect’ – lag between E(x) and S(x) – seems more important

25

The Third World (Then & Now)?

• 5 “poor” (c.1900 or now) countries• 3 Latin America (Argentina, Brazil, Chile)• 2 Asia (Japan, India)

• Progress in both expected life & inequality

• But more inter-country variability than first world• In levels at any point in time• Less or no convergence • In lag of inequality behind expected life

26

Expected Life & SD Log Life: 5 Countries

Expected Life Standard Deviation Log Life at Birth

27Heavy line is average of 10 rich countries shown earlier

Russian Anomaly

• Every country (in range from US to India) has increased LE since c. 1950 • Except FSU/Russia

• LE: - 4 yrs beginning in 1950s, accelerates in 1990s• Reverses previous relative progress• Gap now 10 (females) to 20 (males) years at birth

• Occurs despite continued reduction in infant mortality• Similar Anomalies in Inequality Measures

28

LE at Birth. FSU/Russia Relative to 18 OECD Countries

29

Russian Anomaly

• Every country (in range from US to India) has increased LE since c. 1950 • Except FSU/Russia

• LE: - 4 yrs beginning in 1950s, accelerates in 1990s• Reverses previous relative progress• Gap now 10 (females) to 20 (males) years at birth

• Occurs despite continued reduction in infant mortality• Similar Anomalies in Inequality Measures

• Major effects on Males > 50 since 1990• 1896: LE for 50 yr old male = 18.3 yrs• 2002: LE for 50 yr old male = 17.6 yrs

30

Male to Female LE at 50. FSU/RU, since 1950

31

The Female Advantage

• Today: Female life expectancy ~ 1.07 x Male LE

• C. 1750: Female LE ~ 1.07 Male LE

• But considerable variation in between• 20th century: inverted U

• Antibiotics (favors females) then Heart Disease (favors males)

32

Female to Male Life Expectancy at Birth(average across countries, wars removed)

33

The Female Advantage

• Today: Female life expectancy ~ 1.07 x Male LE

• C. 1750: Female LE ~ 1.07 Male LE

• But considerable variation in between• 20th century: inverted U

• Antibiotics (favors females) then Heart Disease (favors males)

• Also considerable variation across countries• Post WW2: average peaks at ~ 1980 • But ~ 1970 in US/UK, 1980 in FR and 1990 in GE

34

Female to Male LE: 4 Largest Countries, 1950-2002

35

The Female Advantage

• Today: Female life expectancy ~ 1.07 x Male LE

• C. 1750: Female LE ~ 1.07 Male LE

• But considerable variation in between• 20th century: inverted U

• Antibiotics (favors females) then Heart Disease (favors males)

• Also considerable variation across countries• Post WW2: average peaks at ~ 1980 • But ~ 1970 in US/UK, 1980 in FR and 1990 in GE

• Conclusion: “Female advantage” mitigates lower market income• But no clear trends over very long periods 36

In Conclusion

• Economists study income inequality intensively

• Also study the value of life

• Missing a key linkage: improvement in mortality has done more for social equality than all the explicit redistribution.

• But further substantial change in (developed world) inequality unlikely• Without increase in maximum life span• Prob of surviving to 80 > .5• Prob of 80 yr old surviving to 95 ~ .1

• But that kind of change could reverse long decline in mortality inequality37